Page 162 - Aircraft Stuctures for Engineering Student
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146 Bending of thin plates
Fig. 5.1 6 Calculation of shear strain corresponding to bending deflection.
(aw/dy)Sy and the angle DC2Cl is awlax. Thus C1D is equal to
aw aw
--
ax aybY
and the angle DACl representing the shear strain corresponding to the bending
displacement w is
aw aw
--
ax ay
so that the work done on the element by the shear force NxySx is
1 aw aw
- NXySx - -
2 ax ay
Similarly, the work done by the shear force Nxy6y is
1 aw aw
-N S --
2 xy yax ay
and the total work done taken over the complete plate is
It follows immediately that the potential energy of the Nxy loads is
awaw
V =-'r/ 2Nxy-- dx dy (5.44)
xy 2 0 0 ax ay
and for the complete in-plane loading system we have, from Eqs (5.42), (5.43) and
(5.44), a potential energy of
+
v = -'rr 200 [.. ( g)2 Ny( $)2 + ax ay (5.45)
